The present invention relates to the error correction coding and decoding of two-dimensional multilevel signals.
In digital transmission, one approach to decreasing transmission errors involves error correction coding. There have not been such error signal correction coding schemes suitable for two-dimensional multilevel signals for which differential coding is commonly used so that the modulated data stream is immune to carrier phase ambiguities. For the modulated signal (for example, multilevel quadrature amplitude modulation signal), there are some problems to be settled from the aspect of the error correction coding.
One problem resides in the fact that, due to the differential coding an error introduced to a given symbol during transmission would affect another symbol, thereby multiplying itself prior to reception.
Another problem resides in the fact that due to the two-dimensional multilevel signal space it becomes inefficient to provide equal error-correction capability uniformly to all data bits. More specifically, in the quadratic data format an error at a given data point tends to correlate with another error at a different data point and there is a higher degree of correlation between nearby data points than the degree of correlation between remote data points. Thus, the coding technique must take this fact into account in an efficient manner. It has been the usual practice to provide error-correction encoding prior to differential coding and provide error-correction decoding after differential decoding. This prior art method, however, requires a high degree of error-correction capability to cope with the error's self-multiplying nature, thus resulting in inefficient, costly equipment.